So familiar has the calendar become that people tend to forget that it, too, had to be invented. Early farmers needed to know when to plow and sow ahead of rainy seasons, and to time other seasonal activities. Early priests in Babylonia, Egypt, China and other countries, even among the Maya in America, examined therefore the motions of the Sun, Moons and planets across the sky, and came up with a variety of calendars, some still in use.

The Day

The basic unit is obviously the day: 24 hours, 1440 minutes, 86400 seconds, each second slightly longer than the average heartbeat. The day is defined by the motion of the Sun across the sky, and a convenient benchmark is noon, the time when the Sun is at its highest (i. e. most distant from the horizon) and is also exactly south or north of the observer.

"One day" can therefore be conveniently defined as the time from one noon to the next. A sundial can track the Sun's motion across the sky by the shadow of a rod or fin ("gnomon") pointing to the celestial pole (click here for construction of a folded-paper sundial), allowing the day to be divided into hours and smaller units. Noon is the time when the shadow points exactly south (or north) and is at its shortest.

What then is the period of the Earth's rotation around its axis? A day, you say? Not quite.

Suppose we observe the position of a star in the sky--for instance Sirius, the brightest of the lot. One full rotation of the Earth is the time it takes for the star to return to its original position (of course, we are the ones that move, not the star). That is almost how the day is defined, but with one big difference: for the day, the point of reference is not a star fixed in the firmament, but the Sun, whose position in the sky slowly changes. During the year the Sun traces a full circle around the sky, so that if we keep a separate count of "Sirius days" and "Sun days", at the end of the year the numbers will differ by 1. We will get 366. 2422 "star days" but only 365. 2422 Sun days.

It is the "star day" (sidereal day) which gives the rotation period of the Earth, and it is about 4 minutes shy of 24 hours. A clockwork designed to make a telescope follow the stars makes one full rotation per sidereal day.

The clocks we know and use, though, are based on the solar day--more precisely, on the average solar day, because the time from noon to noon can vary as the Earth moves in its orbit around the Sun. By Kepler's laws (discussed in a later section) that orbit is slightly elliptical. The distance from the Sun therefore varies slightly, and by Kepler's second law, the motion speeds up when nearer to the Sun and slows down when further away. Such variations can make "sun-dial time" fast or slow, by up to about 15 minutes.

Very precise atomic clocks nowadays tell us that the day is gradually getting longer. The culprits are the tides, twin waves raised in the Earth's ocean by (mainly) the Moon's gravitational pull. As the waves travel around the Earth, they break against shorelines and shallow seas, and thus give up their energy: theory suggests that this energy comes out of the (kinetic) energy of the Earth's rotational motion.

The Year

The year is the time needed by the Earth for one full orbit around the Sun. At the end of that time, the Earth is back to the same point in its orbit, and the Sun is therefore back to the same apparent position in the sky.

It takes the Earth 365. 2422 days to complete its circuit (average solar days), and any calendar whose year differs from this number will gradually wander through the seasons. The ancient Roman calendar had 355 days but added a month every 2 or 4 years: it wasn't good enough, and by the time Julius Caesar became ruler of Rome, it had slipped by three months.

In 46 BC Caesar introduced a new calendar, named after him the Julian calendar. It is similar to the one used today: the same 12 months, and an added day at the end of February every 4th year ("leap year"), on years whose number is divisible by 4. Two years afterwards the 5th month of the Roman year was renamed July, in honor of Julius. The name of his successor, Augustus Caesar, was later attached to the month following July.

The Julian calendar thus assumes a year of 365. 25 days, leaving unaccounted a difference of 0. 0078 days or about 1/128 of a day. Thus the calendar still slips, but at a very slow rate, about one day in 128 years. By 1582 that slippage was approaching two weeks and Pope Gregory the 13th therefore decreed a modified calendar, named after him the Gregorian calendar. Henceforth years ending in two zeros, such as 1700, 1800, 1900--would not be leap years, except when the number of centuries was divisible by 4, such as 2000. This took away 3 "leap days" every 400 years, i. e. one day per 133 1/3 years--close enough to the required correction of one day per 128 years.

But it was not enough to modify the calendar: a one-time jump of dates was also needed, to get rid of the accumulated difference. In Italy this was done soon after the pope's edict, and "Tibaldo and the Hole in the Calendar" by Abner Shimony spins the story of a boy whose birthday was on a day skipped by that jump. Another birthday affected was that of George Washington, born 11 February 1732: when the British empire in September 1952 implemented the Gregorian calendar, the 11th of February "old style" became the 22nd of February "new style," and nowadays that is when Washington's birthday is usually celebrated.

In Russia the change came only after the revolution, which is why the Soviet government used to celebrate the anniversary of the "October Revolution" on November 7th. The Russian orthodox church continues to use the Julian calendar and celebrates Christmas and Easter about 2 weeks later than most of the Christian world.

Though the count of Persian years starts, like the Moslem one, from the flight of Mohammed to Medina in 622, establishing there the first strong base of Islam, the new year starts at the spring equinox, March 21, with the holiday of Nowruz.

How Nowruz is celebrated:

In Iran, the biggest holiday is Nowruz, New Year's Day.... It always begins on the first day of spring at the exact moment of the equinox. This means that every year Nowruz begins at a different time. One year it might be March 21 at 5:32 A.M., while the next year it might occur on March 20 at 11:54 P.M. Every Iranian knows the exact moment the jubilation begins.

The festivities are preceded by weeks of preparation. Everyone thoroughly cleans his house, buys or makes new clothes, and bakes traditional pastries. A ceremonial setting called a haftseen, which consists of seven symbols beginning with the sound "s," is displayed with other meaningful objects like mirror, colored eggs, and goldfish in a bowl. The objects represent health, renewal, prosperity, fertility and the usual universal hopes shared by people at any New Year's celebration....

For Nowruz, most businesses close and the streets are deserted. For twelve days after equinox, people visit relatives and friends, always starting with the eldest. Once all the elders have been visited, they in turn visit the younger members of the family. At every house, a tray of homemade sweets is offered along with wishes for the new year. Children receive money, always in the form of brand-new bills. I assume that since the wave of immigration after 1980 [the revolution in Iran] banks in America have noticed a sudden increase in demand for crisp bills in the month of March.

[from "Funny in Farsi -- A Memoir of Growing Up Iranian in America" by Firoozeh Dumas, 187 pp., $21.95, Villard Books 2003. A charming, sunny book about growing up in two cultures.]

Some people claim that the Jewish custom of the Passover plate is related to the Persian haftseen. That is a ceremonial plate with seven (or six) symbolic objects, the centerpiece of the table at the Passover dinner, perhaps the most important celebration of the Jewish year, commemorating an ancient event coinciding with the spring equinox.

The Persian year itself has 12 months--the first 6 have 31 days, the next 5 have 30 days, and the last has 28 or 29, depending on whether the year is or isn't a leap year. Each month corresponds to a sign of the zodiac. The number of days in each month (if not the order of months) is therefore the same as in the Western civil calendar. The difference is in the rule for determining leap year, which is more complex. Even the original Jalali calendar was more accurate than the Gregorian one; the current version assigns 683 leap years in a cycle of 2820 years and would take two million years before it shows a one-day inaccuracy!

Their astronomy was well developed, and they noted the "zenial days" when the Sun was directly overhead ("at zenith") and a vertical stick cast no shadow. Their year had 365 days, but in the absence of leap years it slowly shifted with respect to the solstices. That year was divided into 18 named "months" of 20 days each (numbered from 0 to 19), plus the "short month" of Wayeb, whose days were considered unlucky.

Yucatan does not experience summer and winter the way middle latitudes do (e.g. Europe or most of the US), and therefore the Maya calendar was not strongly tied to the seasons the way ours is. The planet Venus received major attention, and its cycles were accurately measured by Maya astronomers. In addition the Maya also observed a "ritual year" of 260 days, consisting of 20 named "long weeks" of 13 numbered days each.

For more--much more!--see here,
here and also
here,, the last being one of a series of web pages devoted to different calendars. About the Maya and Venus, see the chapter "Bringing Culture to the Physicists", p. 313 in "Surely You're Joking, Mr. Feynman!" by Richard Feynman

The Year 2012 and all that

In the first decade of the 21st century the notion spread that some cosmic catastrophe would occur at the winter solstice (21 December) of 2012. It seems to be based on the "long count" Maya calendar, the 13th cycle of which ends that day. I have received and answered many messages on this topic, and some of that correspondence is linked below

It seems to be merely a superstition. What catastrophe, exactly? Some of my correspondents suggested the Earth may reverse rotation (contrary to laws of mechanics), may reverse magnetic polarity (as has happened in the distant geological past, though not so suddenly, and apparently with no effect on life), that an errant planet may strike ours (no evidence of it so far) or that the galaxy might produce a burst of deadly radiation as we cross its equator. A film "2012" due to be released next week is to illustrate graphically what might happen.

Not only has modern science no evidence for such calamity, but it is hard to see how the Maya could have detected the approach of any cosmic event like those mentioned (though they might have had their own superstitions!) They were a stone-age culture with no iron and therefore no idea of magnetism, no way of telling that the galaxy was a huge wheel of stars (Galileo found that with his telescope), probably no good idea that the Earth itself was a huge sphere held together by its gravity.

Exploring Further:

"Tibaldo and the Hole in the Calendar" by Abner Shimony, 165 pp, Copernicus 1998. The book tells the story of a boy in 16th-century Italy whose birthday celebration was set for one of the "lost" days, skipped over by the one-time jump in the calendar which Pope Gregory the 13th ordered. Reviewed by Stephen Battersby in Nature, p. 460, 3 April 1998, and by David Mermin in Physics Today, p. 63, June 1998.